Looking to fight back, her lawyer Alessandro Gamberini told Reuters that she would deposit a defamation suit on Friday against Salvini, who also serves as deputy prime minister and is head of the anti-migrant League party.
"When it comes to offensive, defamatory and hate-provoking statements like those of the minister, the only way that the judge can stop it is by blocking the accounts," Gamberini said.
Rackete is in hiding in an undisclosed location in Sicily and has said she has faced threats of death and violence on social media after she brought her German-flagged Sea-Watch 3 charity ship into the port of Lampedusa last month.
Salvini, who has promised to expel Rackete from Italy, dismissed the threat to be blocked from key social media.
"The German communist, the one who rammed the police patrol boat, has asked the prosecutor to close my Facebook and Twitter pages. There is no limit to absurdity," he wrote on Twitter.
"So can I only use Instagram?" he added.
Rackete's boat hit a patrol vessel as she entered Lampedusa port. She later apologized saying it was an accident and a judge this month dismissed accusations that she had endangered the lives of Italian servicemen.
"Matteo Salvini has publicly and repeatedly called me arrogant, an outlaw, an accomplice to people smugglers, a potential murderer, a delinquent, a criminal, a pirate ... the serious damage to my honor is obvious," Rackete is quoted as saying in the law suit, a copy of which was seen by Reuters.
Salvini has built much of his success on social media and has by far the highest number of followers of any Italian political leader -- with 3.8 million backers on Facebook and 1.1 million on Twitter.
Pollsters say the very public row with Rackete, which enabled Salvini to brandish his hardline, anti-migrant stance, appears to have given him a fresh boost in the polls.
A survey published by polling firm YouTrend on Thursday put the League on some 37.7%, up from the 34.3% it scored at May's European Parliament election -- its best ever ballot-box result.
Since the start of 2019, some 3.165 people have reached Italy but during the last month arrivals from northern Africa have picked up pace, convincing the government to throw more resources into its fight against immigration.